In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

The discus throwing event is one of the complex events in athletics, and it is characterized by a performance method that depends on the principle of mechanical moments and requires high explosive capabilities of the thrower in addition to some physical specifications,which depends effectively and effectively on the biomechanical aspects in generating large moments during rotation. The importance of the research is highlighted by the interest in athletics, especially the effectiveness of the discus throw and the continuation of its development process, the importance of kinetic analysis in revealing the most important weaknesses and strengths of shooters, and the importance of explosive power And the moments generated in the rotation of the

ان دراسة الدين العام في اقتصاد ريعي شديد الارتباط بسوق خارجية شديدة التقلب يعد من الدراسات الحساسة كونها تضع امام الباحثين القيود المالية التي سيتكبل بها اقتصاد ضعيف قليل التنوع يعتمد على سوق الطاقة مما يفقد حالة الاستدامة المالية وتفقد الدولة القدرة على الوفاء بالتزاماتها المالية ، ان الحدود الامنة للدين العام يجب ان تكون بنسبة لا تتجاوز 60% من الناتج المحلي الاجمالي حسب اتفاقية ماسترخت الخاصة بمجلس الاتحا

The role of teacher of kindergarten plays an important role in the educational institution for kindergarten role in  the educational institution  for kindergarten and the failure of its role in the development of the mental processes  of children kindergarten means failing in this institution .and hence the importance and effectiveness of the role of the student applied section kindergarten application period it is there fore necessary to be aware of the importance of learning. in preschool and good professional setting and enjoy a significant level of psychological and social systems and mental qualities and study is the urgent need to find generations hare systematic thinker's mind so stay away from memorization and trad

This research is qualitative in nature. It aims to investigate descriptively, analytically, and comparatively the modern AK model represented by the Sudan Open University Series, and the European framework, the common reference for Teaching Foreign Languages, to uncover what was achieved in them in terms of communication and language use. Accordingly, an integrated, multi-media approach has been adopted to enable the production and reception activities, and the spread of Arabic in vast areas of the world. Such a spread helps Arabic language to be in a hegemonic position with the other living languages. The study is based on getting benefit from human experiences and joint work in the field of teaching Arabic to non-Arabic speakers to mee

The current research aims to identify the perceptual speed of the university students as well as to identify the differences in the level of perceptual speed for the university students according to the variables of (male, female) specialization (scientific, human) university (Baghdad, Mustansiriya). Additionally, the research aims to identify the prevalence of emotional pattern and to identify the relationship between perceptual speed and the emotional patterns among university students. The researcher designed a questionnaire to measure the Emotional Patterns based on Jerome Freedman perspective. As for perceptual speed, the researcher adopted French, Extrom and Price scale (1963), which was tran

Background: The discriminative power of the classical WHO parameters in relation to male fertility is quite low, because they only address few aspects of sperm quality and function. This has led investigators to focus their attention on the male gamete and in particular its genome.Objective: To explore which of the sperm DNA damage parameters measured by comet assay are more reliable, and their relations with the standard semen parameters.Methods: Study was done on 40 infertile men selected from couples attending the Institute of Embryo Reasearch and Infertility Treatment at Al-Kadhimiya City/ Baghdad in the period between February 2009 and May 2009, with a history of infertility of ≥1 years; and 15 healthy volunteers of proven fertili

words of God the Quranic text , is genera words have many faces and connotations a ccording to references, cutures and Ages.That the Quranic text is fixed , But the connotations are moveable the scientists agreed about the miracle of the Qurantic text , But they differd of the Position of miracLe including the muatazala and Al- Ashaira who have adopted the idea of sytem and miracle of linguistic . Most of them were lingustics, grammerians and writers as: AL- Jahith, AL- Faraa Abivbeida , Ibn kutaba , AL -Rumani , AL -katabi , AL- Bakilaai , AL- Gargani and Others.
They also differed in what the words of Allaah mean . Is the Quranic text creature or updated ,it is the issue that exhausted the effort.of muslim scientists though its imbo

Postmodern arguments, formed a critic case of what modernity brought in several levels. Postmodern practice was considered as a proactive case having amorphous concepts and features to what entiled as an intellectual trends postmodern philosophically and intellectually. But, what postmodernism architecture broughts in it essence, was not isolation from the intellectual context and entrepreneurship case, and it was not disconnecting from the intellectual and philosophical era of that period. Lliteratures and philosophical argument precede what (Robert Venturi) and (Charles A Jencks) had brought, albeit it was closer to critics and correction the path of modernity from crystallizing a direction that exceeds modrinity to wh

Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.